I recently read the biography of the mathematian Pascal who was homeschooled by his father after his mother died. His father didn’t think any subject should be taught until the child could easily master it. So he removed all the math books until the children were at least 16 years old. At 12 years old Pascal studied math (in secret) and figured out that the sum of 3 angles in any triangle is 180. His father was so impressed that he allowed him to study Euclid, and by age 16 the boy was the first to prove some new geometry theorems which he presented to, among others, Descartes. His work has influenced philosophers and scientists including Descartes and Isaac Newton. Even his sister was a gifted poet.
This is a good example of what you are writing about concerning delaying formal math.
Saying this is a good example of delayed formal math instruction,…well…it certainly is an example of someone delaying formal instruction, but does not seem to me to be a good example of the success which might result.
Better, instead, is it an example of a genius mind which cannot be contained by circumstances.
What does anyone else think of my observation?
I think the more important thing to note here is that the delay did not by any means put him at a disadvantage.
Doubtless he had a natural aptitude for math. This is clear, but had he tried to learn it earlier, when it would’ve been more difficult, maybe he would have developed a distaste for math and had no desire to pursue it.
We can’t tell, can we, what might have happened? It does seem a loving plan of Pascal’s father to hold off introducing a subject until his children could easily master it.
Does readiness + desire – undo frustration = genius?